In this section we turn to a different concept of calculating the dilepton emission from strongly interacting processes.
The goal is to describe radiation not based on single collision or decay process but to take thermal averages of such processes.
As a result one obtains so-called emissivities, that is an expression for the number of dileptons emitted with given four-momentum and per unit of four-volume (\(d^4x\) ) out of strongly interacting matter with fixed microscopic composition (or equation of state).
Dilepton radiation rates from QCD matter in thermal equilibrium have been first derived for a perturbative gas of quarks and gluons.
The rates can be expressed in accordance with the general expression for coupling leptons to the electromagnetic current of hadrons (cf. Eq. REF ) as [1]}:
\(\frac{dN^{\ell \ell }}{d^4 x}=-4e^4\int \frac{d^3 k_1}{(2\pi )^32E_1}\frac{d^3 k_2}{(2\pi )^32E_2}L_{\mu \nu }(q)\frac{1}{q^4}W^{\mu \nu }(q)\,.\) 
